Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.

Correct result:

V = 44790.6808 cm³

Solution:

a_{1} = 30 cm a_{2} = 12 cm s = 41 cm n = 6 S_{1} = n \cdot \sqrt{3} / 4 \cdot a_{1}^{2} = 6 \cdot \sqrt{3} / 4 \cdot 3 0^{2} = 1350 \sqrt{3} {cm}^{2} ≐ 2338.2686 {cm}^{2} S_{2} = n \cdot \sqrt{3} / 4 \cdot a_{2}^{2} = 6 \cdot \sqrt{3} / 4 \cdot 1 2^{2} = 216 \sqrt{3} {cm}^{2} ≐ 374.123 {cm}^{2} x = \sqrt{s^{2} - (a_{1} - a_{2})^{2}} = \sqrt{4 1^{2} - (30 - 12)^{2}} = \sqrt{1357} cm ≐ 36.8375 cm h_{2} = x \cdot a_{2} / (a_{1} - a_{2}) = 36.8375 \cdot 12 / (30 - 12) ≐ 24.5583 cm h_{1} = x + h_{2} = 36.8375 + 24.5583 ≐ 61.3958 cm V_{1} = S_{1} \cdot h_{1} / 3 = 2338.2686 \cdot 61.3958 / 3 ≐ 47853.2914 {cm}^{3} V_{2} = S_{2} \cdot h_{2} / 3 = 374.123 \cdot 24.5583 / 3 = 48 \sqrt{4071} {cm}^{3} ≐ 3062.6107 {cm}^{3} V = V_{1} - V_{2} = 47853.2914 - 3062.6107 = 44790.6808 {cm}^{3} = 4.479 \cdot 1 0^{4} {cm}^{3}

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